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Math Problems
Algebra 1
Evaluate integers raised to rational exponents
cos
[
tan
−
1
(
−
5
12
)
]
=
\cos \left[\tan ^{-1}\left(-\frac{5}{12}\right)\right]=
cos
[
tan
−
1
(
−
12
5
)
]
=
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Subtract. Write your answer in scientific notation.
\newline
(
1.67
×
1
0
3
)
−
(
9.7
×
1
0
2
)
\left(1.67 \times 10^{3}\right)-\left(9.7 \times 10^{2}\right)
(
1.67
×
1
0
3
)
−
(
9.7
×
1
0
2
)
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(-x)
5
5
5
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Fill in the blank with
>
>
>
,
<
<
<
or
=
=
=
sign.
\newline
45
45
45
−
-
−
(
−
11
)
(-11)
(
−
11
)
______
57
57
57
+
+
+
(
−
4
)
(-4)
(
−
4
)
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-
5
5
5
+ (
7
7
7
\times
9
9
9
)
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-
5
5
5
+ (
7
7
7
\times
9
9
9
)
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(
12
12
12
+
13
13
13
\sqrt{
2
2
2
})-(
−
10
-10
−
10
+
19
19
19
\sqrt{
2
2
2
})
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(
12
12
12
+
13
13
13
\sqrt{
2
2
2
})-(
−
10
-10
−
10
+
19
19
19
\sqrt{
2
2
2
})
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Multiply and simplify the following complex numbers:
(
3
−
4
i
)
×
(
−
3
+
2
i
)
(3-4i) \times (-3 + 2i)
(
3
−
4
i
)
×
(
−
3
+
2
i
)
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Estimate. Which sign makes the statement true?
\newline
448
÷
61
6
448 \div \frac{61}{6}
448
÷
6
61
?
?
?
34
34
34
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
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Estimate. Which sign makes the statement true?
\newline
6
?
211
2
÷
6
6 \, ? \, \frac{211}{2} \div 6
6
?
2
211
÷
6
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
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f
′
(
x
)
f'(x)
f
′
(
x
)
=
12
e
x
12e^x
12
e
x
and
f
(
4
)
f(4)
f
(
4
)
=
−
16
+
12
e
4
-16 + 12e^4
−
16
+
12
e
4
. Find
f
(
0
)
f(0)
f
(
0
)
.
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x
3
−
2
x
+
4
÷
x
−
2
x^{3}-2x+4\div x-2
x
3
−
2
x
+
4
÷
x
−
2
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f
(
x
)
=
4
x
3
+
x
−
1
f(x)=\frac{4}{x^{3}}+\sqrt{x}-1
f
(
x
)
=
x
3
4
+
x
−
1
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Evaluate:
−
40
+
(
−
1
)
−
(
2
)
×
6
÷
3
−
2
- 40 +{ (-1)- (2)} \times 6 \div{ 3-2}
−
40
+
(
−
1
)
−
(
2
)
×
6
÷
3
−
2
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Perform the following operations in the proper order.
\newline
19
+
18
÷
(
−
3
)
−
6
(
5
)
19+18 \div(-3)-6(5)
19
+
18
÷
(
−
3
)
−
6
(
5
)
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What is the value of the expression shown below when
x
=
7
x=7
x
=
7
?
\newline
3
x
2
−
2
x
+
3
3x^{2}-2x+3
3
x
2
−
2
x
+
3
\newline
A
31
31
31
\newline
B
50
50
50
\newline
C
136
136
136
\newline
D
164
164
164
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Solve each of the following using factoring.
\newline
50
x
3
+
125
x
2
−
18
x
−
45
=
0
50x^{3}+125x^{2}-18x-45=0
50
x
3
+
125
x
2
−
18
x
−
45
=
0
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Subtract:
\newline
−
4
x
+
1
-4x+1
−
4
x
+
1
from
−
7
x
2
+
4
x
+
2
-7x^{2}+4x+ 2
−
7
x
2
+
4
x
+
2
\newline
\newline
◻
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∫
y
(
1
−
1
y
)
d
y
\int \sqrt{y}\left(1-\frac{1}{y}\right) d y
∫
y
(
1
−
y
1
)
d
y
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Simplify the expression:
−
9
+
(
2
−
x
)
+
8
x
-9+ (2 - x) + 8x
−
9
+
(
2
−
x
)
+
8
x
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What could be the value of
x
x
x
in the following equation? Select all that apply.
\newline
x
3
=
1
125
x^3 = \frac{1}{125}
x
3
=
125
1
\newline
Multi-select Choices:
\newline
(A)
−
1
125
3
-\sqrt[3]{\frac{1}{125}}
−
3
125
1
\newline
(B)
−
1
5
-\frac{1}{5}
−
5
1
\newline
(C)
1
5
\frac{1}{5}
5
1
\newline
(D)
1
125
3
\sqrt[3]{\frac{1}{125}}
3
125
1
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What could be the value of
x
x
x
in the following equation? Select all that apply.
\newline
x
3
=
1
27
x^3 = \frac{1}{27}
x
3
=
27
1
\newline
Multi-select Choices:
\newline
(A)
1
27
3
\sqrt[3]{\frac{1}{27}}
3
27
1
\newline
(B)
1
3
\frac{1}{3}
3
1
\newline
(C)
−
1
27
3
-\sqrt[3]{\frac{1}{27}}
−
3
27
1
\newline
(D)
−
1
3
-\frac{1}{3}
−
3
1
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Evaluate:
−
6
−
(
−
3
)
-6 - (-3)
−
6
−
(
−
3
)
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What is the value of
2
tan
−
1
(
1
2
)
2\tan^{-1} \left(\frac{1}{2}\right)
2
tan
−
1
(
2
1
)
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8
(
−
6
+
x
)
=
−
112
8(-6+x)=-112
8
(
−
6
+
x
)
=
−
112
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Simplify.
\newline
5
−
x
×
2
5
2
y
12
5
−
x
3
\frac{5^{-x} \times 25^{2 y}}{125^{-\frac{x}{3}}}
12
5
−
3
x
5
−
x
×
2
5
2
y
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Simplify.
\newline
9
2
y
×
3
y
2
7
−
y
3
\frac{9^{2 y} \times 3^{y}}{27^{-\frac{y}{3}}}
2
7
−
3
y
9
2
y
×
3
y
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Simplify.
\newline
(
8
x
5
y
−
1
4
y
8
)
\left(\frac{8x^{5}y^{-1}}{4y^{8}}\right)
(
4
y
8
8
x
5
y
−
1
)
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Simplify.
\newline
9
9
−
4
/
5
\frac{9}{9^{-4 / 5}}
9
−
4/5
9
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∫
sin
4
(
5
x
)
d
x
\int \sin ^{4}(5 x) d x
∫
sin
4
(
5
x
)
d
x
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Find the y-intercept of the line
y
=
1
4
x
+
1
y=\dfrac{1}{4}x+1
y
=
4
1
x
+
1
.
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Simplify.
\newline
(
−
2
x
4
y
5
)
3
\left(-2 x^{4} y^{5}\right)^{3}
(
−
2
x
4
y
5
)
3
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Simplify:
\newline
−
2
7
×
(
−
3
5
8
)
-\frac{2}{7} \times\left(-3 \frac{5}{8}\right)
−
7
2
×
(
−
3
8
5
)
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Simplify:
\newline
x
8
x
3
\frac{x^{8}}{x^{3}}
x
3
x
8
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50
÷
(
−
5
)
50\div(-5)
50
÷
(
−
5
)
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v)
a
+
4
a
2
+
3
a
−
4
\frac{a+4}{a^{2}+3 a-4}
a
2
+
3
a
−
4
a
+
4
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8
2
×
7
2
:
4
2
8^{2} \times 7^{2}: 4^{2}
8
2
×
7
2
:
4
2
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Write the following as a radical expression.
\newline
v
6
7
v^{\frac{6}{7}}
v
7
6
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Assuming that
x
x
x
is in the appropriate domain, find a formula for
\newline
h
−
1
(
x
)
=
1
−
(
sin
−
1
(
(
−
8
−
x
)
2
)
)
h^{-1}(x)=1-\left(\sin ^{-1}\left(\frac{(-8-x)}{2}\right)\right)
h
−
1
(
x
)
=
1
−
(
sin
−
1
(
2
(
−
8
−
x
)
)
)
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−
(
−
1
)
⌊
1
2
+
1
π
⌋
⋅
(
−
π
⋅
⌊
1
2
+
1
π
⌋
+
1
)
\sqrt{-(-1)^{\left\lfloor\frac{1}{2}+\frac{1}{\pi}\right\rfloor} \cdot\left(-\pi \cdot\left\lfloor\frac{1}{2}+\frac{1}{\pi}\right\rfloor+1\right)}
−
(
−
1
)
⌊
2
1
+
π
1
⌋
⋅
(
−
π
⋅
⌊
2
1
+
π
1
⌋
+
1
)
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Convert into decimal form.
\newline
11
−
5
\frac{11}{-5}
−
5
11
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3
∫
1
2
x
2
d
x
3 \int_{1}^{2} x^{2} d x
3
∫
1
2
x
2
d
x
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x
7
⋅
x
4
x^{7} \cdot x^{4}
x
7
⋅
x
4
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ln
(
x
2
+
1
−
x
)
\ln \left(\sqrt{x^{2}+1}-x\right)
ln
(
x
2
+
1
−
x
)
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−
1
9
10
−
3
5
7
-1 \frac{9}{10}-3 \frac{5}{7}
−
1
10
9
−
3
7
5
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x
2
−
1
x
2
−
5
x
+
4
\frac{x^{2}-1}{x^{2}-5 x+4}
x
2
−
5
x
+
4
x
2
−
1
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Find the coefficient of
x
7
x^7
x
7
in the expansion of
(
1
−
x
)
12
(1-x)^{12}
(
1
−
x
)
12
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−
8
a
11
3
\sqrt[3]{-8 a^{11}}
3
−
8
a
11
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(
3
x
y
4
)
3
\left(3 x y^{4}\right)^{3}
(
3
x
y
4
)
3
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1
2
3
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